Question

factorise the given polynomial (x^2-x)^2 - 8 (x^2-x) + 12​

Answer 1

(x2-x)2-8(x2-x)+12

Let (x2-x) =y

y2-8y+12

y2-(6+2)y+12

y2-6y-2y+12

y(y-6)-2(y-6)

(y-6)(y-2)

(x2-x-6)(x2-x-2)

{x2-(3-2)x-6}{x2-(2-1)x-2}

{x2-3x+2x-6}{x2-2x+x-2}

{x(x-3)+2(x-3)}{x(x-2)+1(x-2)}

(x-3)(x+2)(x-2)(x+1)